Hi, this is difficult to recognize given the condition it’s in. What I can make out tentatively looks like a Wolf Spider (Lycosidae), more specifically Tigrosa helluo. They’re not really an indoor species so are likely wandering in somewhere by mistake. If they’re thriving in your basement than there is likely some other bugs down there they’re preying on. You can reduce the number of spiders you see by sealing cracks around floors, doors, windows, foundation, etc., vacuum everywhere and empty the canister outside.

Have you discussed it with the owner of the building? I don’t know if you have legal protections, your basement probably isn’t considered an “ occupied living space.” My rental neighbors work deals with their landlord where they provide the labor if he pays for materials. The landlord gets a discounted upgrade to his property that way. Itsy Bitsy mentioned things you can do that probably wouldn’t even be noticed bu the owner, like weatherstripping around basement windows and a doorsweep on the exterior door. The spider isn’t aggressive. It shouldn’t bite unless it is handled roughly. The kids can… Read more »

The only potentially harmful spider in your region is the black widow which is relatively easy to ID by being globular, black(very dark brown) and having a red hourglass on its underside. There’s no brown recluse that far north, and all other spiders might be creepy but they are not harmful, they do a good job of catching other ‘pests’ around our homes and gardens.